Nuprl Lemma : prime_imp_atomic
∀[a:ℤ]. atomic(a) supposing prime(a)
Proof
Definitions occuring in Statement :
prime: prime(a),
atomic: atomic(a),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
atomic: atomic(a),
prime: prime(a),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
or: P ∨ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
reducible: reducible(a),
exists: ∃x:A. B[x],
int_nzero: ℤ-o,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal-wf-base,
int_subtype_base,
assoced_wf,
reducible_wf,
not_wf,
divides_wf,
all_wf,
or_wf,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal,
divides_reflexivity,
self_divisor_mul,
mul_com
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
independent_pairFormation,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
because_Cache,
extract_by_obid,
isectElimination,
intEquality,
applyEquality,
baseClosed,
natural_numberEquality,
Error :productIsType,
Error :universeIsType,
Error :functionIsType,
Error :inhabitedIsType,
multiplyEquality,
Error :unionIsType,
isect_memberEquality,
voidElimination,
productEquality,
functionEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
setElimination,
rename,
independent_functionElimination,
imageElimination,
imageMemberEquality,
instantiate,
universeEquality,
independent_isectElimination,
unionElimination,
hyp_replacement,
applyLambdaEquality
Latex:
\mforall{}[a:\mBbbZ{}]. atomic(a) supposing prime(a)
Date html generated:
2019_06_20-PM-02_23_01
Last ObjectModification:
2018_09_26-PM-05_56_30
Theory : num_thy_1
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