Nuprl Lemma : order-type-less-transitive
Trans(WFO{i:l}();x,y.order-type-less() x y)
Proof
Definitions occuring in Statement :
WFO: WFO{i:l}(),
order-type-less: order-type-less(),
trans: Trans(T;x,y.E[x; y]),
apply: f a
Definitions unfolded in proof :
trans: Trans(T;x,y.E[x; y]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
order-type-less: order-type-less(),
WFO: WFO{i:l}(),
spreadn: spread3,
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
order-preserving: order-preserving(A;B;a1,a2.R1[a1; a2];b1,b2.R2[b1; b2];f),
compose: f o g,
cand: A c∧ B,
prop: ℙ,
infix_ap: x f y,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Lemmas referenced :
compose_wf,
and_wf,
order-preserving_wf,
all_wf,
exists_wf,
order-type-less_wf,
WFO_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
sqequalRule,
productElimination,
thin,
dependent_pairFormation,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
applyEquality,
independent_pairFormation,
because_Cache,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
Trans(WFO\{i:l\}();x,y.order-type-less() x y)
Date html generated:
2016_05_15-PM-04_13_54
Last ObjectModification:
2015_12_27-PM-02_59_15
Theory : general
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