Nuprl Lemma : qeq-trans
Trans(ℤ ⋃ (ℤ × ℤ-o);r,s.qeq(r;s) = tt)
Proof
Definitions occuring in Statement :
qeq: qeq(r;s),
trans: Trans(T;x,y.E[x; y]),
int_nzero: ℤ-o,
b-union: A ⋃ B,
btrue: tt,
bool: 𝔹,
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
trans: Trans(T;x,y.E[x; y]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
qeq-functionality,
equal_wf,
bool_wf,
qeq_wf,
btrue_wf,
b-union_wf,
int_nzero_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
equalityTransitivity,
intEquality,
productEquality
Latex:
Trans(\mBbbZ{} \mcup{} (\mBbbZ{} \mtimes{} \mBbbZ{}\msupminus{}\msupzero{});r,s.qeq(r;s) = tt)
Date html generated:
2016_05_15-PM-10_36_46
Last ObjectModification:
2015_12_27-PM-08_01_12
Theory : rationals
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