Nuprl Lemma : assoced_weakening
∀a,b:ℤ. a ~ b supposing a = b ∈ ℤ
Proof
Definitions occuring in Statement :
assoced: a ~ b,
uimplies: b supposing a,
all: ∀x:A. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
assoced: a ~ b,
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal-wf-base,
int_subtype_base,
divides_wf,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal,
divides_reflexivity
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
Error :isect_memberFormation_alt,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
independent_pairFormation,
Error :universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
hypothesisEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_functionElimination,
because_Cache
Latex:
\mforall{}a,b:\mBbbZ{}. a \msim{} b supposing a = b
Date html generated:
2019_06_20-PM-02_20_57
Last ObjectModification:
2018_09_26-PM-05_47_57
Theory : num_thy_1
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