Nuprl Lemma : ocmon_connex
∀g:OCMon. ∀x,y:|g|. ((↑(x ≤b y)) ∨ (↑(y ≤b x)))
Proof
Definitions occuring in Statement :
ocmon: OCMon,
grp_le: ≤b,
grp_car: |g|,
assert: ↑b,
infix_ap: x f y,
all: ∀x:A. B[x],
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
and: P ∧ Q,
ulinorder: UniformLinorder(T;x,y.R[x; y]),
uorder: UniformOrder(T;x,y.R[x; y]),
eqfun_p: IsEqFun(T;eq),
monot: monot(T;x,y.R[x; y];f),
cancel: Cancel(T;S;op),
connex: Connex(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y])
Lemmas referenced :
ocmon_properties,
ocmon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
sqequalRule
Latex:
\mforall{}g:OCMon. \mforall{}x,y:|g|. ((\muparrow{}(x \mleq{}\msubb{} y)) \mvee{} (\muparrow{}(y \mleq{}\msubb{} x)))
Date html generated:
2016_05_15-PM-00_11_21
Last ObjectModification:
2015_12_26-PM-11_43_31
Theory : groups_1
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