Nuprl Lemma : ringeq_int_terms_weakening
∀[r:Rng]. ∀[t1,t2:int_term()]. t1 ≡ t2 supposing t1 = t2 ∈ int_term()
Proof
Definitions occuring in Statement :
ringeq_int_terms: t1 ≡ t2,
rng: Rng,
int_term: int_term(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
rng: Rng,
prop: ℙ,
and: P ∧ Q,
all: ∀x:A. B[x],
ringeq_int_terms: t1 ≡ t2,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_wf,
rng_car_wf,
ring_term_value_wf,
int_term_wf,
equal_wf,
and_wf
Rules used in proof :
equalityTransitivity,
isect_memberEquality,
intEquality,
functionEquality,
axiomEquality,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
because_Cache,
productElimination,
rename,
setElimination,
applyLambdaEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesisEquality,
independent_pairFormation,
hypothesis,
dependent_set_memberEquality,
equalitySymmetry,
lambdaFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[r:Rng]. \mforall{}[t1,t2:int\_term()]. t1 \mequiv{} t2 supposing t1 = t2
Date html generated:
2018_05_21-PM-03_15_57
Last ObjectModification:
2018_01_25-PM-02_18_25
Theory : rings_1
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