Nuprl Lemma : ringeq_int_terms_wf
∀[t1,t2:int_term()]. ∀[r:Rng]. (t1 ≡ t2 ∈ ℙ)
Proof
Definitions occuring in Statement :
ringeq_int_terms: t1 ≡ t2,
rng: Rng,
int_term: int_term(),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
rng: Rng,
ringeq_int_terms: t1 ≡ t2,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
int_term_wf,
rng_wf,
ring_term_value_wf,
equal_wf,
rng_car_wf,
all_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
applyEquality,
functionExtensionality,
lambdaEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
intEquality,
functionEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[t1,t2:int\_term()]. \mforall{}[r:Rng]. (t1 \mequiv{} t2 \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-03_15_50
Last ObjectModification:
2018_01_25-PM-02_18_16
Theory : rings_1
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