Nuprl Lemma : int-rational
∀[n:ℤ]. (n ∈ ℚ)
Proof
Definitions occuring in Statement :
rationals: ℚ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
squash: ↓T,
prop: ℙ,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
rationals: ℚ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x]
Lemmas referenced :
b-union_wf,
int_nzero_wf,
equal-wf-T-base,
bool_wf,
qeq_wf,
qeq-equiv,
subtype_rel_b-union-left,
equal_wf,
squash_wf,
true_wf,
qeq_refl,
btrue_wf,
iff_weakening_equal,
quotient-member-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
extract_by_obid,
isectElimination,
thin,
productEquality,
lambdaEquality,
hypothesisEquality,
baseClosed,
applyEquality,
because_Cache,
imageElimination,
natural_numberEquality,
imageMemberEquality,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_functionElimination
Latex:
\mforall{}[n:\mBbbZ{}]. (n \mmember{} \mBbbQ{})
Date html generated:
2018_05_21-PM-11_44_08
Last ObjectModification:
2017_07_26-PM-06_42_59
Theory : rationals
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